RESPONSE TO OTHERS:
I disagree with Polymath257 (who is a mathematician who studied the big bang and general relativity). He asserts that the universe is like a sphere that started expanding at pole, and will collapse back (the debunked "oscillating universe" theory). Rather, the universe is expanding, and that expansion is accelerating with no sign that it will ever stop.
Just to be clear, I was giving an analogy. It is a simple version to understand the basic concept. I agree that the 'Big Crunch' version is almost certainly NOT the correct picture.
There are two bisic issues with this analogy: the first, like you said, is that it has a Big Crunch. This is easily fixed by imagining a trumpet shape instead of a sphere.
The other basic issue is that it LOOKS like space is flat and not curved, at least not to a large degree. This is a harder one to find a smaller dimensional analogy with.
Most of the rest of what you say is correct, although there are a couple of subtle points:
ANSWER:
DEFINITION OF EXPLOSION: A stick of dynamite on an indestructible chess board would splatter bits of explosive across the board.
UNIVERSE DIDN'T EXPLODE (CHESS BOARD EXPANDED): The board is called the metric. It is three dimensional. Those familiar with relativity speak of spacetime, but in this case, only space expands, not space and time..
Einstein once said that without matter and energy, space and time would not exist. So, outside of the metric, nothing exists, nothing can exist, time doesn't exist, and nothing from outside of the metric (the universe) can enter the universe.
Nothing can travel across the metric faster than the speed of light (in a vacuum). However, the metric can (and is) expanding so fast, that distant stars travel away faster than the speed of light (they are on the metric, and the metric is expanding faster than the speed of light).
Light from stars that are traveling away at nearly the speed of light have a Doppler red shift. When they exceed the speed of light, no light is seen from them (literally the expansion of the metric is outpacing light itself).
Technically, the red shift is NOT a Doppler shift, although for small velocities it approximates one.
Also, a lot of care is required in the relationship between the Hubble boundary (where the expansion is at light speed) and the edge of the observable universe. For example, we *can* see galaxies that have a red shift corresponding to 'speeds' larger than that of light. Anything with a z value more than 1 qualifies for this. We currently know of galaxies with z>6.
WHY IS THE UNIVERSE ACCELERATING?
No one knows, for sure, what causes the acceleration of the expansion of the universe. Using Friedman's Equation, most physicists, astronomers, and cosmologists assume (unscientific high speculation) that there must be some undiscovered dark energy doing it. I would not disagree, nor would I agree (and I refrain from speculation, though would support experiments to look at the idea). That dark energy is though to have antigravity (repulsive) properties. I'd sooner believe that empty free space has antigravity. CERN (subatomic particle accelerator in Switzerland) has an experiment to see if perhaps antimatter exploded in front of the matter universe, and is now exerting anti-gravity. To this end, in the year 2020, they have suspended a subatomic antiparticle in a magnetic field, removed the field and timed its drop (to see if antimatter has the same type of gravity as matter). The results are that antimatter's gravity "so far appears" to be the same as matter's gravity. Thus, it is unlikely that antimatter is the cause of antigravity which might cause the expansion of the universe.
No, the accelerating expansion is certainly NOT due to antimatter.
There is a history here. Einstein introduced a 'cosmological constant' to allow for a static universe because he didn't like the prediction his equations made for a non-static one (expanding or contracting). After the expansion was discovered, he called adding this in his biggest mistake.
Well, the acceleration of the expansion seems to be due to a cosmological constant that is different in value that what Einstein proposed. In essence, to have a static universe, some sort of repulsive aspect of gravity is required. A different value produces accelerating expansion.
What is interesting is that the CC corresponds to a energy density for a vacuum: an amount of energy that is present in a vacuum even if nothing else is there.